# Solution

1. $$[\mathrm{high}]_o(x)=[\mathrm{high}]_o(x)$$
2. $$[\mathrm{low}]_o(x)=[\mathrm{low}]_o(x)$$
3. $$[\mathrm{nasal}]_o(x)=[\mathrm{nasal}]_o(x)$$
4. $$[\mathrm{ATR}]_o(x)= \begin{array}[t]{l} \mathtt{if}~[\mathrm{low}]_i(x)~\mathtt{then}~\top~\mathtt{else}\\ \mathtt{if}~[+\mathrm{ATR},+\mathrm{hi}]_i(s(x))~\mathtt{then}~\top~\mathtt{else}\\ \mathtt{if}~[+\mathrm{ATR},-\mathrm{hi},-\mathrm{lo},-\mathrm{nas}]_o(s(x))~\mathtt{then}~\top~\mathtt{else}\\ [\mathtt{ATR}]_i(x) \end{array}$$